A chimera state in a homogeneous spatiotemporal dynamical system is an asymmetric pattern consisting of the coexistence of synchronized and desynchronized domains. This phenomenon has attracted increasing attention as it has been discovered in a variety of models and has been demonstrated in experiments. This talk gives a brief review of the research on chimera states and focuses on their occurrence in systems subject to global interactions. We consider a system of globally coupled maps as a model for such systems and study the emergence of clusters and chimera states. We show the relationship between these two collective states and investigate the conditions for their occurrence.